File:Quadrupole-potential-contour-xy.svg
Summary
| Description |
English: Contour plot of the equipotential surfaces of an electric quadrupole field of a point-like quadrupole. The field is accurately computed from a physical model. The quadrupole tensor is . |
| Date | |
| Source | Own work |
| Author | Geek3 |
| SVG development | |
| Source code | Python codeimport numpy as np
from matplotlib import pyplot as plt
from matplotlib import colors
def simplify_contours(qcset, thresh=plt.rcParams['path.simplify_threshold']):
for c in qcset.collections:
paths = c.get_paths()
for i, p in enumerate(paths):
p.simplify_threshold = thresh / plt.gcf().dpi
paths[i] = p.cleaned(simplify=True)
# quadrupole tensor of positive charges in xy-direction and negative in -xy
Q = np.array([[0, 6., 0], [6., 0, 0], [0, 0, 0]])
xmax = 3.2
vmax = 0.15
ngrid = 400
levels = np.linspace(-vmax, vmax, 22)
XYZ = np.mgrid[-xmax:xmax:ngrid*1j, -xmax:xmax:ngrid*1j, 0:0:1j]
X, Y = XYZ[0,:,:,0], XYZ[1,:,:,0]
V = np.zeros_like(X)
for i in range(ngrid):
for j in range(ngrid):
r = XYZ[:,i,j,0]
d = np.linalg.norm(r)
V[i,j] = 0.5 * r.dot(Q).dot(r) / (4. * np.pi * d**5)
V = np.clip(V, -2.*vmax, 2.*vmax)
plt.figure(figsize=(6, 6)).add_axes([0, 0, 1, 1])
contf = plt.contourf(X, Y, V, levels=levels, cmap='RdBu_r', extend='both',
norm=colors.SymLogNorm(linthresh=0.07, vmin=-vmax, vmax=vmax))
simplify_contours(contf, 0.9*plt.rcParams['lines.linewidth'])
cont = plt.contour(X, Y, V, levels=contf.levels, colors='k', linestyles='solid')
plt.xticks([]), plt.yticks([])
plt.gca().set_aspect(aspect='equal')
plt.gca().axis('off')
for i in -1,1:
for j in -1,1:
plt.text(.2*i, .2*j, {-1:u'\u2212', 1:'+'}[i*j],
size=18, ha='center', va='center')
plt.savefig('Quadrupole-potential-contour-xy.svg')
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